[FOM] Earliest known computing language

[John Kadvany]

FOM readers may be interested in my paper now publishedonline at History and Philosophy of Logic, ‘Panini’s Grammar and ModernComputation’ (preprint at academia.edu). The paper is mostly expository and is intended for audiences familiarwith modern formalisms and their computational properties.  Panini is the 4th century BCSanskrit linguist famous for his quite formal generative grammar based onPost-style rewrite methods not seen again until the 20thcentury.   The abstract below explains why  I characterize Panini’s grammar as theearliest known computing language, here meaning a generative formalism capableof expressing universal computation.  Building on existing scholarship, new here areobservations relating Panini to Post’s rewrite techniques and reasons why thegrammar, while intended for oral recitation, almost surely relied on alphabeticwriting.    John Kadvany   Abstract: Panini's Grammar and Modern Computation Panini’s fourth (?) century BC Sanskrit grammar uses rewriterules utilizing an explicit formal language defined through a semi-formalmetalanguage. The grammar is generative, meaning that it is capable ofexpressing a potential infinity of well-formed Sanskrit sentences starting froma finite symbolic inventory. The grammar’s operational rules involve extensiveuse of auxiliary markers, in the form of Sanskrit phonemes, to control grammaticalderivations. Panini’s rules often utilize a generic context-sensitive format toidentify terms used in replacement, modification or deletion operations. Thecontext-sensitive rule format is itself defined using Panini’s more general methodof auxiliary markers, the latter used to define many dozens of linguisticcategories and rules controlling derivations of Sanskrit sentences through themanipulation of ‘non-terminal’ and ‘terminal’ symbols.  This technique for controlling formalderivations was rediscovered by Emil Post in the 1920s and later shown by him tobe capable of representing universal computation. The same implicitcomputational strength of Panini’s formalism follows as a consequence: while Panini’sSanskrit grammar is computationally limited, the metalanguage through which hisformalism is defined can be directly used to define any rule-based system bymimicking standard formal language definitions as an extension of thegrammatical system proper. Panini’s formal achievement is historicallydistinctive, as derivations of grammatically correct, spoken Sanskrit, are designedfor oral recitation, with the grammar itself constructed as an organic extensionof the spoken object language. Panini’s formulation of what amounts to anorally realized symbolic calculus stands in contrast to the implicitinscriptional methods of contemporary formalisms, such as Gottlob Frege’sappropriately named Begriffsschrift andthe early computing paradigms of Post and Alan Turing. Nonetheless, contemporaryviews on the cognitive status of phonemic recognition and historical writingsystems support the conjecture that, in spite of Panini’s rigorous oralformulation, construction of the grammar almost surely relied on alphabeticwriting.        
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